Common Factor the Great Defeats the Candy Zombies!

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SWBAT use the distributive property to factor variable expressions.

Big Idea

Students will start factoring out multiplication over subtraction.

Warm up

15 minutes

This warmup stealing candy from zombies refers to the story I tell students when we first start learning about distributive property in an earlier lesson (Halloween Candy to Zombies) in which I distribute a certain number of candies to each group of trick or treaters (zombies) that come to my door. For example 3 candies each to one group of 4 and to another group with an unknown number of trick-or-treaters (x) looks like 3(4+x). They learn to multiply to distribute the candy to all the groups that come into my doorway. This is a context that makes the distributive property a little more engaging and comprehensible to middle school students. It also gives them a real world context that helps make sense of each term in the expressions.

In this warm up students are given variable expressions and are asked what is the largest amount of candies I could have distributed to each of the Zombies, so they have to factor.The first three problems are all addition. Some students may still be factoring just fine, but not finding the greatest common factor. I may need to still review with some of them how to test the remaining terms inside the parentheses for common factors by asking if I could have distributed a larger number of candies. If no one is making a mistake I may do it on purpose and ask what they would tell me to prove that I did not find the greatest common factor.

The fourth problem is subtraction and I ask students if this last group of zombies is getting any candy. I remind them that these are the naughty zombies and that Comon Factor the Great is taking back their candy.  

The last problem gives students a polynomial and are told that it represents groups of zombies leaving my house after receiving candy. I ask how many candies I distributed to each zombie. I ask this questions for two reasons.

  • I want to see if they are simplifying the expression first, if not I suggest they do so.
  • I also want to make sure they are not stopping after they combine like terms.

If students give me 8x+ 14 as the final answer I ask them if this solution answers the question of how many candies I distributed to each. I may also need to remind them that these terms represent the zombies after I have given them candy, so they have to factor. 

White boards

39 minutes

For the white boards students work on one problem at a time in their math family groups and everyone shows me their answer at the count of three. This way, no one can opt out and I can give individual feedback.

First I have them work on factoring out the greatest common factor over subtraction with the following:

27x - 14          16x - 24          24x - 32         12c + 8e - 16    

I circulate to help them check that they have found the greatest common factor, by having them look at the terms remaining inside the parentheses and checking for common factors. I may say "do you see how these two terms still share a common factor? That means you have not found Common Factor the Great! He's still hiding!" I purposely do not have a variable term being subtracted, because students don't know yet how to represent a negative number when they try to write it in the standard order.

If most students are successful I will tell them that sometimes we need to simplify our expressions before we can factor:

10x + 10y + 5x + 2y          4c + 40 + 3c + 9       5 + 2x + x + 4 + 5 + 4x 

To challenge some students I will give them a choice to either work on the second problem above or make up a problem like the last two that we can challenge the class with, then I use the expressions they give me. It is possible that their expression can't be factored if they were not careful in choosing their terms. I will ask the class what changes we could make so that it could be a factorable problem. This really has students look closely at the relationships between the numbers. It also engages them in the practices of attending to precision and also in critiquing the arguments of others.

For the remainder of class I let them work on homework factoring subtraction together as I circulate.